In DE 10 2009 034 095 A1 and EP 1 261 992 B1, humidifiers for fuel cells are described which have a plurality of superimposed membranes which separate flow channels for the feed-through of moist and dry air. Water molecules penetrate the membranes from the moist to the dry air stream which is thus enriched with moisture. The exhaust gas of the fuel cell can be used as moist incoming air stream; the moisture of which exhaust gas is transferred through the membrane into a fresh-air stream which is then fed to the inlet of the fuel cell system in order to generate current in an electrochemical reaction.